Thank you for your question. The history of multiplication can be traced back to several different early civilisations. These included Egyptian, Greek, Chinese and Indian civilisations.
It is understood that the Egyptian modality of multiplication involved a process of successive additions and doubling. This involved a heavy reliance on breaking down multiplications to their core and adding them in successions to achieve their answers.
During this period of civilisation, they were said to use what is known as a 'sexagesimal positional number system.' This is a primordial program of the more current decimal system. Babylonians employed the method of using multiplication tables, which assisted in achieving multiplications of higher numbers that were too difficult to be done alone.
The history of multiplication in Chinese civilisation dates back to before 300BC. It involved subtraction, division, multiplication and place value addition. Al Khwarizmi is said to have introduced such modalities of mathematics to Arab countries subsequent to these discoveries.
I hope this answers your question.